In 1927, during the formative years of quantum mechanics, Friedrich Hund posed a paradox: Why is a chiral molecule found in either its left-handed or right-handed isomeric forms and not in a superposition of the two? After all, both isomers are equally likely. At first glance, the answer seems clear. If the tunneling time between the two isomers is long, their superposition is unlikely to arise. That answer might hold for a sugar, protein, or other large chiral molecule, whose tunneling time may exceed the age of the universe, but it fails for small molecules. Nor can it explain why the habitual states of a molecule, large or small, are its left-handed and right-handed isomers and not its energy or parity eigenstates. Now, Klaus Hornberger and Johannes Trost of Ludwig-Maximilians University in Munich have resolved Hund's venerable paradox. The two theoreticians analyzed the case of one of the smallest chiral molecules, deuterium disulphide (shown here), tumbling in and buffeted by a monoatomic gas. The calculation uncovered a surprisingly large phase-dependence in the scattering amplitude that distinguishes the two isomers. Thanks to the phase difference, the ambient gas atoms can pick out the states that correspond to the molecule's left-handed and right-handed isomers far more readily than the molecule’s other states. When the first few atoms strike a molecule, it's knocked into either its left-handed or right-handed configurational state. Further atomic bombardment acts on the molecule like repeated quantum measurements, keeping it in its chiral state. (J. Trost, K. Hornberger, Phys. Rev. Lett. 103, 023202, 2009.) —Charles Day
Resolving an 82-year-old quantum paradox
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I am not sure if this paper exactly "resolved Hund's venerable paradox." From the account above, it seems that Hornberger and Trost have shown (and this is quite interesting) that interactions with atoms of the monoatomic gas imposes structure on the molecule. Many years ago, R.G. Wooley asked the question "Must a molecule have a shape?" A molecule in isolation may indeed have a highly delocalized distribution of nuclei (as in the central panel of the figure shown) and need not have a definite chirality. I have read somewhere that certain low pressure mass spectrometry experiments have revealed structures that are highly delocalized. If anyone knows about these, and can point me to the literature, I would be very grateful.
Small molecules are indeed known to be in angular momentum and parity eigenstates (just as electrons in atoms). That is, their nuclei are not localized.
Only large molecules are strongly affected by decoherence in such a way that their nuclei are localized (not their electrons!). It depends on the strength of the interaction with the environment and the level density. There is an intermediate range where only states which differ in parity or angular momentum (rotational bands) are affected by decoherence, thus giving rise to chiral or oriented states, while the various energy eigenstates possess the same "intrinsic" structure: they are different superpositions of different orientations and chiralities of one and the same localized state.
It then follows from the intrinsic symmetry of the ammonia molecule, for example, that you need spin 3 to get different parity eigenstates (forming the famous maser mode).
Best regards,
Dieter Zeh